The present invention relates to direction finding and, more particularly, to a method and apparatus for determining the orientation of a body, such as a vehicle or a theodolite, relative to a local geographic coordinate system.
Many methods and devices are known for determining the geographic heading of a body such as a vehicle. Magnetic compasses, which are among the oldest of such devices, find the direction of magnetic north, rather than geographic north, so their readings must be corrected for the local deviation of magnetic north from geographic north. More modern methods and devices include gyrocompasses and methods based on signals received from external transmitters such as the GPS satellite network. Gyrocompassing performance (accuracy and duration) is very sensitive to a gyroscope""s drift. The process is very long, usually lasting between 10 minutes and 40 minutes. For high accuracy, a very expensive gyroscope must be used. The methods based on external signals are, by definition, not autonomous.
The object of the present invention is more general than merely finding local north. The object of the present invention is the determination of the full three-dimensional orientation of a body with respect to local geographic coordinates. The local geographic Cartesian coordinate system is the xe2x80x9clocal level local northxe2x80x9d (LLLN) coordinate system, in which the x-axis points towards local north, the y-axis points towards local east and the z-axis points down. The body itself has its own Cartesian coordinate system, referred to herein as the xe2x80x9cbody coordinate systemxe2x80x9d. For example, a typical Cartesian coordinate system for a vehicle is x-axis=forward, y-axis=right and z-axis=down. The orientation of the body is defined in terms of the Euler angles through which a Cartesian coordinate system, initially aligned with the LLLN coordinate system, must be rotated to align that Cartesian coordinate system with the body coordinate system. These Euler angles are azimuth xcexa8, pitch "THgr" and roll "PHgr". The rotations that bring the coordinate system, that initially is aligned with the LLLN coordinate system, into alignment with the body coordinate system, are:
1. rotation of the x and y axes by azimuth xcexa8 about the z-axis;
2. rotation of the x and z axes by pitch "THgr" about the intermediate y-axis to bring the x-axis into coincidence with the body x-axis; and
3. rotation about the x-axis by roll "PHgr" to bring the y and z axes into coincidence with the body y and z axes.
Note that azimuth xcexa8 also is the angle between geographic north and the projection of the body x-axis in the horizontal (x-y) LLLN plane.
According to the present invention there is provided a method of determining an orientation of a body, including the steps of: (a) measuring an acceleration of the body in a first direction; (b) measuring an acceleration of the body in a second direction different from the first direction, the first direction and the second direction defining a plane; (c) measuring an acceleration perpendicular to the plane in a coordinate system rotating about an axis perpendicular to the plane; and (d) inferring the orientation of the body from the three measurements.
According to the present invention there is provided a method of determining an azimuth of a body, the azimuth being defined in a certain plane, the method including the steps of: (a) measuring an acceleration, perpendicular to the plane, in a coordinate system rotating about an axis perpendicular to the plane; and (b) inferring the orientation of the body from the measured acceleration.
According to the present invention there is provided an apparatus for determining an orientation of a body, including: (a) a first accelerometer, fixedly mounted with respect to the body, for measuring an acceleration of the body in a first direction; (b) a second accelerometer, fixedly mounted with respect to the body, for measuring an acceleration of the body in a second direction, the first and second directions defining a plane; (c) a third accelerometer for measuring an acceleration in a direction perpendicular to the plane; and (d) a mechanism for revolving the third accelerometer about an axis of revolution perpendicular to the plane.
According to the present invention there is provided an apparatus for determining an azimuth of a body, the azimuth being defined in a certain plane, including: (a) a first accelerometer, for measuring an acceleration perpendicular to the plane; and (b) a mechanism for revolving the first accelerometer about an axis of revolution perpendicular to the plane.
The present invention exploits the fact that the LLLN coordinate system is rotating. Specifically, the LLLN coordinate system rotates, along with the Earth, around the Earth""s rotational axis, at a uniform (vectorial) angular velocity {right arrow over (xcexa9)}. This fact is exploited to determine the azimuth angle of a body that is stationary with respect to the Earth. The principle of the present invention, in its most general form, is to measure acceleration in the body z-direction, using an accelerometer that is caused to revolve, at a uniform angular speed, around an axis of revolution, that itself points in the body z-direction, at a fixed distance from the axis of revolution. Because this accelerometer is moving with respect to the Earth, the acceleration measured by this accelerometer includes a Coriolis force component. Meanwhile, the components of the gravitational acceleration of the body in the body x- and y- directions are measured by two other accelerometers. Because the body is stationary with respect to the Earth, the accelerations in the x- and y- directions do not include a Coriolis component. The pitch and roll are inferred from the measured x- and y- accelerations. The azimuth is inferred from the pitch, the roll, and the phase of the time-dependent part of the acceleration in the z-direction. In the special case of zero pitch and zero roll, only the acceleration in the z-direction is measured, and the phase of the time-dependent part of the acceleration in the z-direction is identical to the azimuth.
Preferably, to reduce sensitivity to common mode noise sources such as vibration, two accelerometers, on opposite sides of the axis of revolution, are used to measure the acceleration in the z-direction. The signals of the two accelerometers are subtracted.
The method of the present invention for defining the azimuth is relatively insensitive to common accelerometer errors such as constant bias, scale factor error, and misalignment errors.
Unlike magnetic compasses, the present invention is independent of the Earth""s magnetic field. Unlike methods that rely on external transmitters such as GPS satellites, the present invention is fully autonomous. A drawback of the present invention relative to gyrocompasses is that the present invention works only for a stationary body; but bodies oriented using gyrocompasses must themselves be stationary when gyrocompassing is performed.